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C₂×#62355 #10577649

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(13,19)(15,20)(17,24)(18,23)(21,25)(22,26);(3,5)(4,7)(6,10)(8,9)(11,12,16,14)(13,17,22,21)(15,18,20,23)(19,24,26,25);(11,13,20,26,16,22,15,19)(12,17,23,25,14,21,18,24);(5,10)(7,9)(11,14,16,12)(13,21,22,17)(15,23,20,18)(19,25,26,24);(4,8)(7,9)(12,14)(13,22)(18,23)(19,26)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484845);